Turbines are widely used in a variety of aviation, industrial, and power generation applications to perform work. Each turbine generally includes alternating stages of peripherally mounted stator vanes and axially mounted rotating blades. The stator vanes may be attached to a stationary component such as a casing that surrounds the turbine, while the rotating blades may be attached to a rotor located along an axial centerline of the turbine. The stator vanes and rotating blades each have an airfoil shape, with a concave pressure side, a convex suction side, and leading and trailing edges. In addition, conventional rotating blades are mechanically stacked such that the center of gravity of each section coincides axially and/or tangentially with an airfoil hub center of gravity. A compressed working fluid, such as steam, combustion gases, or air, flows along a gas path through the turbine. The stator vanes accelerate and direct the compressed working fluid onto the subsequent stage of rotating blades to impart motion to the rotating blades, thus turning the rotor and performing work.
Various conditions may affect the maximum power output of the turbine. For example, colder ambient temperatures generally increase the differential pressure of the compressed working fluid across the turbine. As the differential pressure of the compressed working fluid across the turbine increases, the velocity of the compressed working fluid over the suction side of the rotating blade increases, creating considerable shock waves and corresponding shock losses at the trailing edge of the rotating blades. At a sufficient differential pressure, the shock waves and corresponding shock losses at the trailing edge of the rotating blades may prevent the rotating blades from increasing the amount of work being extracted from the compressed working fluid. At a sufficient differential pressure, the shock waves become tangential to the trailing edge, creating a condition known as limit load. The strong shock now goes from the trailing edge of one airfoil to the trailing edge of the adjacent airfoil. The resultant shock losses may prevent the rotating blades from increasing the amount of work being extracted from the compressed working fluid as the maximum tangential force is reached. If the pressure ratio increases beyond the limit load, a drastic increase in loss occurs. As a result, the maximum power output of the turbine may be limited by colder ambient temperatures.
Various systems and methods have been developed to reduce the shock losses across the rotating blades. For example, the geometric shape of the airfoil and the size of the gas path directly affect the velocity of the compressed working fluid, and thus the shock losses, across the rotating blades. However, the geometric shape of the airfoil can only reduce the shock losses to a certain extent. In addition, the size of the gas path is generally constrained by other design limits and is generally fixed after manufacture of the turbine. Therefore, an improved turbine and method for reducing shock losses in the turbine would be useful, especially for uprates, where an increase in flow and hence Mach number exists.